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amina_soneviseth

  • one year ago

how can i find the sum of three consecutive numbers

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  1. mathstudent55
    • one year ago
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    You mean they are unknown, and you need to write an equation?

  2. SolomonZelman
    • one year ago
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    If the lowest integer is x, then the second one is (x+1) and the third one is (x+2). The sum would be = `x + (x+1) + (x+2)` = x + x + x + 1 + 2 = `3x+3`

  3. amina_soneviseth
    • one year ago
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    sorry i meant the sum of three consecutive even integers of -54 how do i find the answer?

  4. mathstudent55
    • one year ago
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    Since they are even, then the difference between them is 2. Use the idea that @SolomonZelman gave you, but modify it this way: Let the smallest number be x. Then the next larger number is x + 2 The largest of the three numbers is x + 4. The sum then is: x + x + 2 + x + 4 Set that sum equal to -54. Then solve for x. That gives you the smallest number. Then add 2 to x to find the middle number, and add 4 to x to find the largest number.

  5. amina_soneviseth
    • one year ago
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    i dont understand, why x? and how do i get to the answer thank you

  6. freckles
    • one year ago
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    Let's say you have the number 2. And I ask you what is the next even number after 2, you would say 2+2 or 4 right? And if I asked for the third even number after 2, you would say 2+4 or 6 right? Let's say you have the number x. (assume x is even) The next even number after x, would be x+2. The third even number after x, would be x+4. The sum of these numbers would be (x)+(x+2)+(x+4) or dropping the ( ) you could say x+x+2+x+4 and you want this to be equal to -54 as you said above... So you have the equation x+x+2+x+4=-54 to solve. So you will need to first combine your like terms on the left hand side. That is do you know what x+x+x=? and you should know 2+4=6...

  7. amina_soneviseth
    • one year ago
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    so its x+x+x+2+4= -54? where do i go from there? :D

  8. IrishBoy123
    • one year ago
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    on the left- hand side of your equation: A/ add up the x's B/ add up the numbers

  9. IrishBoy123
    • one year ago
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    IOW, simplify it a bit... :p

  10. mathstudent55
    • one year ago
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    In math (Algebra) we use letters (called variables) to represent unknown amounts. Since we don't know what the three even numbers are, we use the letter x, here called a variable, to represent the smallest of the three unknown even numbers. Once we choose x to represent the smallest of three even numbers, the other two even numbers are x + 2 and x + 4, as explained in an earlier response above. The sum of the three numbers is -54, so we can write this as an equation: x + x + 2 + x + 4 = -54 We now combine all x's on the left side. x is the same as 1x 1x + 1x + 2 + 1x + 4 = -54 1x + 1x + 1x + 2 + 4 = -54 Adding 1x + 1x + 1x, we get 3x; also, 2 + 4 = 6, so we now have 3x + 6 = -54 Now we need to subtract 6 from both sides of the equation. 3x + 6 = -54 - 6 -6 -------------- 3x = -60 Now we divide both sides by 3 to get: 3x/3 = -60/3 x = -20 Since x represents the smallest of the three numbers, now we know that the smallest of the 3 consecutive even numbers is -20. The next number is x + 2 = -20 + 2 = -18 The largest of the 3 number is x + 4 = -20 + 4 = -16 The numbers are -20, -18, -16 Now let's check. -20, -18, and -16 are consecutive even numbers. What is -20 + (-18) + (-16) = ? -20 + (-18) + (-16) = -54 The sum of the three numbers is -54, so our answer is correct. The three numbers are -20, -18, and -16.

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